1. Field of the Invention
The present invention relates to a circuit, method, and system in which a transfer characteristic can be generated according to the specific requirements of an application. The transfer characteristic can be in the form of a power (Axn), quadratic (Axn+BXn-1 . . . ), logarithmic (logAB), or any other non-linear form that is approximated by a sum of piece-wise-linear (PWL) functions.
2. Description of the Related Art
For analog scanning processors in a cathode ray tube (CRT), a transfer characteristic of power r (where r can be any real number, for instance from 1.5 to 4.5) is desirable for the horizontal dynamic focus (HDF) section of the scanning processor. This could previously only be realized by cascading several multipliers together, and the power of this transfer characteristic is limited by r being an integer. Moreover, the complexity of using the multiplier configuration will increase if a higher power transfer characteristic is to be realized.
In this section, two different approaches to generating the same transfer characteristics are discussed. Although the discussion touches on the multiplier configuration and the logarithmic-exponential configuration, it can be extended to other configurations or circuits in which any form of transfer characteristics is to be implemented.
The first configuration uses multipliers and switches and is shown in FIG. 1. Switch S1 is used to select the input to the second multiplier block such that the overall transfer characteristic can either have a power of 3 or 4. Switch S2 selects the output signal either from the first or second multiplier block so as to obtain the correct transfer characteristic.
In FIG. 1, the system comprises basic multiplier cells that are only able to produce a transfer characteristic in the form of (Inputr), where the power, r, is limited to an integer number. If a system needs a power that is a real number (i.e., 2.6), a designer will tend to implement the multiplier to provide a power of 2 or 3 as an approximation. If a power of higher order, for example 7 or 8, is to be designed, then the circuit geometry will increase in size and/or complexity. Furthermore, if the system is required to be able to select from a range of power terms, numerous switches have to be implemented to select the inputs for each multiplier, and also to select the desired signal at the output. This will further increase the size of the system.
The second configuration consists of logarithmic-exponential transforms and an amplifier. The transfer characteristic in the form of Input, can be expressed in another form as shown below.f(Input)=Inputr(=er(ln(Input)) In: natural log
With this new representation, it shows that this system can be implemented using another approach. This approach mainly consists of 3 sections, and the block diagram for each section is shown in FIG. 2a. First, a logarithmic transform has to be supplied to the input, where the result of the transform is (ln(Input)). Next, it is necessary to amplify the product with a constant value (r). Finally, an exponential transform is done.
With this approach, a system with a different power term can be generated by controlling the amplification factor in the amplification block. However, there are drawbacks to this approach. A basic logarithmic amplifier is shown in FIG. 2b. This basic logarithmic amplifier consists of an operational amplifier, an input resistor, Rin, that is used to convert the voltage input, Vinput, to a current input, Is, and an NPN transistor that is used to convert the current input to a logarithmic voltage output, Voutput. From the transfer function of this logarithmic block as shown in FIG. 2b, it can be seen that the output is dependent on the process parameter, Is. Moreover, this logarithmic amplifier employs negative feedback, which means that the issue of control stability should be considered. Furthermore, this circuit exhibits a strong temperature dependence due to the thermal voltage, VT as well as Vin/Rin or Is. This dependence can be significantly reduced by using various compensation techniques. These compensation techniques may require extra components to be added, which would increase the circuit geometry.